Detecting frequency modulation in stochastic time series data

We propose a new test to identify non-stationary frequency-modulated stochastic processes from time series data. Our method uses the instantaneous phase as a discriminatory statistics with confidence bands derived from surrogate data. We simulated an oscillatory second-order autoregressive process to evaluate the size and power of the test. We found that the test we propose is able to correctly identify more than 99% of non-stationary data when the frequency of simulated data is doubled after the first half of the time series. Our method is easily interpretable, computationally cheap and does not require choosing hyperparameters that are dependent on the data.